If someone is over eighteen, or if the contract is for necessities, i.e. a place to live, a person is held to contracts that you sign. A contract is a promise made in exchange for a promise. Here the landlord promised to keep the space for your use, and you agreed to pay him rent. He (or she) relied upon your agreement to pay him rent and did not rent the space to another person. If he cannot re-rent the space he will lose money because you are not keeping your promise.
A person should not be required to pay any more than the rent for the time that the space was empty, but the landlord may not have been able to rent it to someone else. All of the students may have found spaces and no-one may need your space.
The lanldor offered a lower rental rate for signing up early: the risk was that plans may change in exchange for the lower rate.